Question

A perfectly competitive firm has a production function ?(?₁, ?₂) = ?₁?₂. Input prices are given by ?₁ = 2 and ?₂ = 1.

a. Does this production function exhibit decreasing, constant, or increasing returns to scale?

b. In the short run, input factor 2 is fixed at x₂=8 and the firm chooses the optimal input quantity x^*₁ to minimize the cost of producing output y=72. Derive x₁^*.

c. Calculate the costs c_s associated with the above short-run solution.

d. In the long-run, the firm chooses the optimal input quantities x₁^* and x₂^* to minimize the cost of producing output y= 72. Write the Lagrangian function for this firm's long-run cost minimization problem.

e Derive the first order conditions for this firm's long-run cost minimization problem.

Answer 1

please give rating it will be appreciable, thank you

the solution of the above question are,